Algebraic Data Types and Self-Reference in Type Theory - From Theory to Version Control

Watch a technical seminar exploring advanced concepts in algebraic data types and their extensions for handling self-referential data structures. Delve into how standard algebraic data types can be enhanced beyond simple lists to handle complex structures like graphs and Petri nets. Learn about two semantic interpretations: one based on groupoids that captures symmetries of self-referential structures, and another focused on data mutation and version control. Understand how this theoretical framework enables structured version control for combinatorial data, with practical applications in software development. Gain insights into how this approach differs from traditional dependent types while achieving similar capabilities for expressing validity constraints. The presentation maintains an accessible overview of these complex mathematical concepts, focusing on the broader implications for data structure design and version control systems rather than detailed mathematical proofs.